Tuesday, 30 December 2014

According to Yahoo, the missing plane QZ8501 may be found at the bottom of the Java Sea. It is not 100% confirmed though. We sincerely hope there are some survivors who may have swum to a nearby island.

“I am absolutely devastated," said AirAsia Group CEO Tony Fernandes. "This is a very difficult moment for all of us at AirAsia as we await further developments of the search and rescue operations but our first priority now is the wellbeing of the family members of those onboard QZ8501."

WordPress creates a nice annual report, detailing crucial statistics about my blog. My blog received up to 200,000 views in 2014! Hoping to hit a million views soon. :P

Predictably, the most popular post turns out to be Free Exam Papers. Shows how useful doing past year papers is!

Sunday seems to be the day which I post the most. Most of the Sundays, I only teach one student after church, hence I have more time to post.

The O Level Formula List post turns out to be the second most popular post in 2014, beating the post about JC Cut Off Points. 3 of my most popular posts were actually written before 2014! Hence, the report claims that those posts have "staying power", and I should consider writing more about them!

It has been a wonderful year and blogging, originally a means to advertise my Maths tuition service, has turned into a hobby for me. I am now letting my WordPress blog self-run on its own for a moment, while building up my Blogger website, hoping that my Adsense application will be finally approved! My final goal is to be active on WordPress, Blogger, and YouTube, publicizing Mathematics!

This is a Javascript application that I wrote a long time ago. It can help to count which are the most common letters in any language，even Chinese!
For instance, try typing "四是四，十是十，十四是十四，四十是四十。 莫把四字说成十，休将十字说成四。 若要分清四十和十四，经常练说十和四。" into the textbox, and press "Generate Report". You will see that the word "四" is being mentioned 11 times!

What are the chances of 3 numbers (taken from the range 1-9999) adding up to 8888?

We will calculate the probability of 3 numbers (between 1 to 9999, since most aeroplane flight numbers are up to four digits) adding up to 8888.

We will first do an analytic theoretical calculation, and then follow up with a numerical simulation to double confirm our calculations.

Theoretical Calculation

Firstly, there are 9999 numbers from 1 to 9999. Hence, in total, there are $9999^3=999700029999$ ways of selecting 3 numbers from the range 1-9999. Repeats are allowed, for example 17, 17, 17, since they could be from different airlines e.g. MH17, QZ17, SQ17, just to illustrate the point.

Next, we need to consider how many positive integer solutions there are to $x_1+x_2+x_3=8888$. One of them would be 17, 370, 8501; but there are many more like 1, 1, 8886.

The technique to solve this type of question is to use a Stars and bars (combinatorics) method.
We can write 8888 stars, and to separate them into 3 "bins" we need 2 bars. Hence, out of 8887 possible gaps, we need to choose two gaps to put the bars. Hence, the total number of ways is ${8887 \choose 2}=39484941$.

Hence, the final probability, the chance of 3 random numbers adding up to 8888 is $$\frac{39484941}{999700029999}=0.0039497\%$$, or around 1 in 25,000.
(WolframAlpha Calculation)

For comparison, this is rarer than winning the top prize in 4D (a popular guess the correct 4 digit number lottery in Singapore), which has a probability of 0.01%, or 1 in 10,000.

My sincerest condolences to all the passengers and families of those taking QZ8501. It is really a tragedy, to have so many air disasters in a short time. As I also travel yearly, I can empathize with all the passengers, the crew, and finally the family and friends of those who took the flight. God bless them, and may they rest in peace.

Eerie Coincidence of Missing Flight Numbers (Math)

Someone from Hardwarezone did a calculation of the flight numbers of the missing flights recently (MH17 + MH370 + QZ8501)

17+370+8501=8888 !!

For Westerners who may not know the significance of 8888, it is one of the most auspicious 4 dight numbers for Chinese, because "8" rhymes with 发 ("fa", "huat", which means prosper). Any car license plate "8888" must have cost a bomb for the owner.

But why does the flight numbers add up to "8888", such an eerie coincidence. Nobody knows...

Excerpts:To keep the math relatively simple and to avoid complications like integrating the partial volume of a sphere, we can approximate Smaug’s bed of gold and silver to be a cone, with a radius of 9.6 feet (1/2 the diameter) and a height of 7 feet (assuming the weight of the dragon will smush down the point of the cone by about a foot).

Thursday, 25 December 2014

J. J. Abrams is making Star Wars Episode 7. He rented three speeder bikes which was 700 imperial credits to start. He must pay 100 imperial credits (EACH) to keep his speeder bikes daily. If he does not pay daily, Prince Xizor and other Black Sun members will kidnap J. J. Abrams, bring him to Mustafar, and sacrifice him.

J. J. Abrams is also paying 5 bounty hunters to keep separatist spies out. That costs 200 imperial credits (EACH) to start, then 50 imperial credits for each bounty hunter every time they capture a spy. The Separatists send 2 spies every day.

In how many days does J. J. Abrams spend the same amount of imperial credits on speeders and bounty hunters?

A kid named Cody decided to set a Math question based on Star Wars, a rather complicated one it seems. J. J. Abrams, the famous director, decided to answer his question (see below)! Very impressive! See, even directors need to use some Math!

Lets try to verify JJ Abrams' answer (2.5 days)! (The question is a bit confusing to be honest, since it does not clearly specify 700 imperial credits is for total or individual speeder bikes. I have added the words (EACH) to make it more clear. But it is a very good job considering it is a small kid!)

Looking for Tutors in Singapore

Maths Tutor

Mr Wu is a patient and dedicated Maths tutor, who has many years of tuition experience. He has tutored students of various levels, ranging from upper primary, secondary, JC, and even university undergraduates.

Mr Wu is a Pure Math Major, having completed his undergraduate studies at NUS and graduating with a First Class Honours.

We really need to salute our Singaporean children for working hard in terms of homework. Singaporeans rank number 3 in terms of the most time spent on homework. 15-year-olds (around Secondary 3 level) clock around 9.4 hours of homework a week, above the global average of 5 hours.

Based on personal experience, students from top elite schools definitely spend much more time on homework. For example, based on my experience as a student and a teacher, it is not abnormal to spend up to 2 hours a day on homework, leading to 14 hours a week of homework.

Students in South Korea actually spend fewer than 3 hours on homework each week, but this is highly suspicious, because the Hagwon culture (cram school) culture in South Korea is very widespread. Hence, though they don't spend much time on homework, they do spend a lot of time on other academic pursuits (tuition, enrichment, etc).

The problem with excessive homework is when students have to sacrifice sleeping time to complete their homework, leading to sleep deprivation, which is very bad for teenagers and even adults in general.

In conclusion, a balance on the amount of time spent on homework is definitely needed.

In Math, we are taught how to use the following prefixes:
kilo: meaning thousand or 10^3
mega: meaning 10^6
giga: meaning 10^9

Hence, theoretically, a kilobyte is 1000 bytes, a megabyte is 10^6 bytes, and a gigabyte is 10^9 bytes.

Now, most computers nowadays have a few gigabytes of memory, most notably 2MB, 4MB or 8MB. However, sometimes this isn't enough, for instance when a user is multitasking or playing some graphic intensive games. This will lead to the dreaded Blue Screen of Death (BSOD), with strange errors such as "Page fault in nonpaged area" which makes no sense to normal users.

How to Solve Blue Screen of Death

Recently, I discovered a way to solve the Blue Screen of Death. Ever since using this method, I have not experienced another Blue Screen of Death on my 4 year old laptop! Hence, I wish to share it with anyone!

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Rule of Thumb: If it ain't broke, don't fix it. If your computer is free of errors, no need to do anything!